Subtraction with multiple digits in each operand can get tricky when you have the case where in one of the columns the first numbers digit is less than the second numbers digit. For problems where the first number is greater than the second number, you can use a technique called borrowing or renaming to perform the subtraction. This involves borrowing a set amount from the column directly to the left of the column you are performing the subtraction on. Lets look at an example:
In the case of this problem the first thing to do is look at the ones column and subtract the first digit from the second; in this case 2-8. Since 2 is smaller than 8 we cannot do the subtraction within the context of this problem. What we need to do is borrow from the tens column. Since the number 42 can be broken down in to 4 sets of 10 and 2 ones, we can take one of those sets of 10 and move them over to the ones column. So now instead of 4 sets of 10 and 2 ones, we have 3 sets of 10 and 12 ones.
We can now subtract the ones place by doing the following problem: 12 - 8 = 4.
We can then subtract the tens column as 3 - 1 = 2.
We now arrive at our answer of 24.
Thinking about it with words.
Another way to think about this problem is spelling out the words of the place values.
4 tens 2 ones
- 1 ten 8 ones
After performing the borrow we get the following:
3 tens 12 ones
- 1 ten 8 ones
We can then subtract the ones place 12 - 8 = 4
3 tens 12 ones
- 1 ten 8 ones
4 ones
followed by the tens place 3 - 1 = 2.
3 tens 12 ones
- 1 ten 8 ones
2 tens 4 ones
We now have our answer of 24.
Borrowing From a Zero
In certain situations you may run across a problem where you need to borrow from a zero. Lets take the following problem as an example:
In this problem, the 6 in the ones column is less than the 8 so we need to borrow from the tens column. Since there is a 0 in the tens column there is nothing to borrow. so what we need to do is borrow 10 tens from the hundreds column
Since we now have 10 tens in the tens column, we can borrow one of those tens and move it to the ones column. Don't forget to cross out that 10 and make it a 9:
We can now subtract each column, 16 - 8 = 8 for the ones column, 9 - 8 = 1 for the tens column and 1-1=0 for the hundreds column to get our final answer of 18
